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Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

Hybrid block method with quasilinearization for the dynamical simulation of a methamphetamine abuse model

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pp. 399–412Vol. 29Issue 2February 2026DOI: 10.47974/JIM-2337XML
Received:
05 Mar 2025
Published Online:
05 Dec 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2337
Pages:
399–412

Abstract

We propose a single-step hybrid block approach that incorporates three strategically chosen fixed off-grid points to tackle a system of methamphetamine abuse models governed by first-order equations. The method is formulated using a polynomial basis formed via a power-series representation and is proven to be both convergent and A-stable. Numerical experiments demonstrate that the proposed method effectively approximates the solution, highlighting its capability to solve the methamphetamine abuse model and other first-order initial value problems. Additionally, we analyze the effect of immigration on the dynamics of methamphetamine abuse and find that controlling user influx is a crucial strategy for mitigating the spread of substance use. These findings emphasize the significance of incorporating immigration control measures into intervention policies to curb methamphetamine abuse effectively. 

Keywords

Subject Classifications

65L0565L0665L2092D2592C50

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